量子顶点代数及其phi-坐标模中的若干问题

本项目主要研究量子顶点代数及其phi-坐标模中的若干问题，研究内容主要分成如下三个方面: (1) 研究量子顶点代数的结构及具体例子，包括与q-形变Clifford代数等例子相关的量子顶点代数，以及一般的量子顶点代数及其phi-坐标模的扭张量积。(2) 研究量子顶点代数的与一般associate 对应的(扭) phi-坐标模的A(V)-理论。(3) 研究与量子仿射代数、Yangian相关联的量子顶点代数及其phi-坐标模。

In this project, we mainly study some problems in quantum vertex algebras and its phi-coordinate modules and the contents can be divided into the following three parts: (1) We will mainly study the structures and concrete examples of quantum vertex algebras, including the quantum vertex algebras related to q-deformed Clifford algebra and other examples, as well as the twisted tensor products of the general quantum vertex algebras and phi-coordinate modules. (2) We shall study the A(V)-theory of (twisted) phi-coordinate modules of quantum vertex algebras corresponding to a general associate. (3) We will study quantum vertex algebras and phi-coordinate modules associated with quantum affine algebras and Yangian.